Percent Increase/Decrease

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Explain this!

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If an investor owns a stock priced at $100 a share, and it moves up two points $2.00), he has made 2 percent on his money.
The same $2 movement in a $200 stock is only a 1 percent gain. Although he gains the same dollar value, the percentage growth of his money is less with the higher-value stock.

Is the 2 percent gain better than the 1 percent gain?
 
When comparing investment gains it matters how much is invested. 'Normalizing' gains as percentage of the invested amount is a good approach to make sure we are comparing apples to apples. So, yes, 2% gain is better than 1%.
 
Explain this! said:
If an investor owns a stock priced at $100 a share, and it moves up two points $2.00), he has made 2 percent on his money.
The same $2 movement in a $200 stock is only a 1 percent gain. Although he gains the same dollar value, the percentage growth of his money is less with the higher-value stock.

Is the 2 percent gain better than the 1 percent gain?
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Goodness gracious.

If you buy one share of a stock priced at $100 per share, you must invest $100. If you buy one share of a stock priced at $200 per share, you must invest $200. If you can afford to buy the stock costing $200 per share, you can afford to buy two shares of the stock costing $100 per share.

Now let's compare what happens if you buy 2 shares of the $100 stock or 1 share of the $200 stock. Remember you have the same amount of money at risk and unavailable. If the $100 stock goes up in price by $2 (a 2% increase) while the $200 stock goes up by $2 (a 1% increase), your investment will be worth $204 if you bought the $100 stock but only $202 if you bought the $200 stock. And obviously, 204 is greater than 202.

If you want to, you can think of the difference in percentage changes as measuring the difference in performances assuming that you made equal investments. It is a way to avoid counting apples and oranges as the same thing.
 
Let's take JeffM's point to the extreme. You invest $100 and make $2 vs investing $1,000,000 and making $2.

If you invest $100, you don't expect (shouldn't) to make much money.

However, if you invest $1,000,000 you might expect to live off the money you make from this investment.

So sure it matters how much you have to invest to make $2.

Suppose I had an offer (that you believed) where you give me $10 and in a week I give you back $1,000+$10. You would quickly give me $10! However, If I said that you have to give me $1,000,000 (and you easily had that much money) and in a week I would give you back $1,000,000 + $1,000 you would not be as eager to do this.

I learned a long time ago from a very non-mathematical friend to look at extremes when you do not see things clearly.

The exact incident went like this. I asked my friend would it matter what year engine you have rebuilt for you car since it would be a new engine anyways? He responded, (in ~1980), well would you like if they rebuilt a 1930 engine and put it in your car? That example totally changed how I think about certain problems in math.
 
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JeffM said:
Goodness gracious.

If you buy one share of a stock priced at $100 per share, you must invest $100. If you buy one share of a stock priced at $200 per share, you must invest $200. If you can afford to buy the stock costing $200 per share, you can afford to buy two shares of the stock costing $100 per share.

Now let's compare what happens if you buy 2 shares of the $100 stock or 1 share of the $200 stock. Remember you have the same amount of money at risk and unavailable. If the $100 stock goes up in price by $2 (a 2% increase) while the $200 stock goes up by $2 (a 1% increase), your investment will be worth $204 if you bought the $100 stock but only $202 if you bought the $200 stock. And obviously, 204 is greater than 202.

If you want to, you can think of the difference in percentage changes as measuring the difference in performances assuming that you made equal investments. It is a way to avoid counting apples and oranges as the same thing.
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I am not understanding something here. The $100 per share increased $2.00, and the $200 per share increased $2.00. They both increased by the same amount. So each increased $2.00. Why would the $102 per share be better than the $202 per share?
 
@Explain this:
Your problem is similar to one that we had awhile ago--it also dealt with percent increase vs. decrease.
The problem solved there might be useful to you. It has an example of a common mistake made in these types of problems.

Here is the link.
 
Explain this! said:
I am not understanding something here. The $100 per share increased $2.00, and the $200 per share increased $2.00. They both increased by the same amount. So each increased $2.00. Why would the $102 per share be better than the $202 per share?
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The $100 investment is better because you can take your $200 and buy 2 $100 shares. Each goes up $2, your total gain will be $4. $4 is better than $2, would you agree?
 
lev888 said:
The $100 investment is better because you can take your $200 and buy 2 $100 shares. Each goes up $2, your total gain will be $4. $4 is better than $2, would you agree?
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lev888 said:
The $100 investment is better because you can take your $200 and buy 2 $100 shares. Each goes up $2, your total gain will be $4. $4 is better than $2, would you agree?
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I think this situation is like comparing fractions. One cannot compare $2/$100 with $2/$200 since $100 is not the same as $200. If $2/$100 is changed to $4/$200, it is easy to compare and know that the $2/$100 has the better growth.

Does this make sense?
 
Explain this! said:
I think this situation is like comparing fractions. One cannot compare $2/$100 with $2/$200 since $100 is not the same as $200. If $2/$100 is changed to $4/$200, it is easy to compare and know that the $2/$100 has the better growth.

Does this make sense?
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Yes, it does.

PROPORTION:
[MATH] {$4}/{$200}[/MATH]=[MATH]$1/$100[/MATH]
 
Explain this! said:
I think this situation is like comparing fractions. One cannot compare $2/$100 with $2/$200 since $100 is not the same as $200. If $2/$100 is changed to $4/$200, it is easy to compare and know that the $2/$100 has the better growth.

Does this make sense?
Click to expand...
That argument was already made to you in post #3 !! Did you read it?
 
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